Shape of the Ground State Energy Density of Hill’s Equation with Nice Gaussian Potential

José A. Ramírez () and Brian Rider ()
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José A. Ramírez: Universidad de Costa Rica
Brian Rider: University of Colorado at Boulder

Journal of Theoretical Probability, 2008, vol. 21, issue 2, 413-430

Abstract: Abstract Consider Hill’s operator $Q=-\frac{d^{2}}{dx^{2}}+q(x)$ in which the potential q(x) is an almost surely continuous and rotation invariant Gaussian process on the circle x∈[0,1). Viewing the classical Riccati map as a change of measure, we establish functional integral formulas for the probability density function of the ground state energy and also determine the density’s shape.

Keywords: Probability Density Function; Ground State Energy; Left Tail; Stationary Gaussian Process; Covariance Kernel (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1007/s10959-007-0105-y

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